<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
<meta http-equiv="X-UA-Compatible" content="IE=9"/>
<meta name="generator" content="Doxygen 1.8.15"/>
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<title>Pepr3D: D:/Home/MFF/1-Mgr/projekt/pepr3d/src/geometry/GeometryUtils.h Source File</title>
<link href="tabs.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="jquery.js"></script>
<script type="text/javascript" src="dynsections.js"></script>
<link href="navtree.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="resize.js"></script>
<script type="text/javascript" src="navtreedata.js"></script>
<script type="text/javascript" src="navtree.js"></script>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
  $(document).ready(initResizable);
/* @license-end */</script>
<link href="search/search.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="search/searchdata.js"></script>
<script type="text/javascript" src="search/search.js"></script>
<link href="doxygen.css" rel="stylesheet" type="text/css" />
</head>
<body>
<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
<div id="titlearea">
<table cellspacing="0" cellpadding="0">
 <tbody>
 <tr style="height: 56px;">
  <td id="projectlogo"><img alt="Logo" src="pepr3d_icon.svg"/></td>
  <td id="projectalign" style="padding-left: 0.5em;">
   <div id="projectname">Pepr3D
   &#160;<span id="projectnumber">v1.0</span>
   </div>
   <div id="projectbrief">Pepr3D is a 3D graphics editor designed for FDM printing</div>
  </td>
 </tr>
 </tbody>
</table>
</div>
<!-- end header part -->
<!-- Generated by Doxygen 1.8.15 -->
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
var searchBox = new SearchBox("searchBox", "search",false,'Search');
/* @license-end */
</script>
<script type="text/javascript" src="menudata.js"></script>
<script type="text/javascript" src="menu.js"></script>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
$(function() {
  initMenu('',true,false,'search.php','Search');
  $(document).ready(function() { init_search(); });
});
/* @license-end */</script>
<div id="main-nav"></div>
</div><!-- top -->
<div id="side-nav" class="ui-resizable side-nav-resizable">
  <div id="nav-tree">
    <div id="nav-tree-contents">
      <div id="nav-sync" class="sync"></div>
    </div>
  </div>
  <div id="splitbar" style="-moz-user-select:none;" 
       class="ui-resizable-handle">
  </div>
</div>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
$(document).ready(function(){initNavTree('_geometry_utils_8h_source.html','');});
/* @license-end */
</script>
<div id="doc-content">
<!-- window showing the filter options -->
<div id="MSearchSelectWindow"
     onmouseover="return searchBox.OnSearchSelectShow()"
     onmouseout="return searchBox.OnSearchSelectHide()"
     onkeydown="return searchBox.OnSearchSelectKey(event)">
</div>

<!-- iframe showing the search results (closed by default) -->
<div id="MSearchResultsWindow">
<iframe src="javascript:void(0)" frameborder="0" 
        name="MSearchResults" id="MSearchResults">
</iframe>
</div>

<div class="header">
  <div class="headertitle">
<div class="title">GeometryUtils.h</div>  </div>
</div><!--header-->
<div class="contents">
<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="preprocessor">#pragma once</span></div><div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;</div><div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="preprocessor">#include &quot;CGAL-patched/Boolean_set_operations_2/Gps_traits_adaptor.h&quot;</span></div><div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment">//---------------------------------------</span></div><div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;</div><div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#include &quot;Triangle.h&quot;</span></div><div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="preprocessor">#include &quot;cinder/Ray.h&quot;</span></div><div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;</div><div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="preprocessor">#include &lt;CGAL/Nef_polyhedron_2.h&gt;</span></div><div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="preprocessor">#include &lt;CGAL/Polygon_2.h&gt;</span></div><div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="preprocessor">#include &lt;CGAL/Polygon_set_2.h&gt;</span></div><div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="preprocessor">#include &lt;CGAL/Polygon_with_holes_2.h&gt;</span></div><div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="preprocessor">#include &lt;CGAL/Simple_cartesian.h&gt;</span></div><div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="preprocessor">#include &lt;optional&gt;</span></div><div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="preprocessor">#include &lt;vector&gt;</span></div><div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;</div><div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="preprocessor">#include &quot;peprassert.h&quot;</span></div><div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;</div><div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespacepepr3d.html">pepr3d</a> {</div><div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;<span class="keyword">class </span>DataTriangle;</div><div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;</div><div class="line"><a name="l00028"></a><span class="lineno"><a class="line" href="classpepr3d_1_1_geometry_utils.html">   28</a></span>&#160;<span class="keyword">class </span><a class="code" href="classpepr3d_1_1_geometry_utils.html">GeometryUtils</a> {</div><div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;   <span class="keyword">private</span>:</div><div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;    <span class="comment">// Prevent this util class from being constructed</span></div><div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;    <a class="code" href="classpepr3d_1_1_geometry_utils.html">GeometryUtils</a>() {}</div><div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;</div><div class="line"><a name="l00033"></a><span class="lineno"><a class="line" href="classpepr3d_1_1_geometry_utils_1_1_tri_ray_int_visitor.html">   33</a></span>&#160;    <span class="keyword">class </span><a class="code" href="classpepr3d_1_1_geometry_utils_1_1_tri_ray_int_visitor.html">TriRayIntVisitor</a> : <span class="keyword">public</span> boost::static_visitor&lt;glm::vec3&gt; {</div><div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;       <span class="keyword">public</span>:</div><div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;        <span class="keyword">inline</span> glm::vec3 operator()(<span class="keyword">const</span> DataTriangle::K::Point_3&amp; pt)<span class="keyword"> const </span>{</div><div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;            <span class="keywordflow">return</span> glm::vec3(static_cast&lt;float&gt;(pt.x()), static_cast&lt;float&gt;(pt.y()), static_cast&lt;float&gt;(pt.z()));</div><div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;        }</div><div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;</div><div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;        <span class="keyword">inline</span> glm::vec3 operator()(<span class="keyword">const</span> DataTriangle::K::Segment_3&amp; seg)<span class="keyword"> const </span>{</div><div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;            <span class="keyword">const</span> <span class="keyword">auto</span> pt = seg.start();</div><div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;            <span class="keywordflow">return</span> glm::vec3(static_cast&lt;float&gt;(pt.x()), static_cast&lt;float&gt;(pt.y()), static_cast&lt;float&gt;(pt.z()));</div><div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;        }</div><div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;    };</div><div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;</div><div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;   <span class="keyword">public</span>:</div><div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;    <span class="keyword">template</span> &lt;<span class="keyword">typename</span> K&gt;</div><div class="line"><a name="l00049"></a><span class="lineno"><a class="line" href="classpepr3d_1_1_geometry_utils.html#a6fe5d1ec681688da1e249a0f87a4944d">   49</a></span>&#160;    <span class="keyword">static</span> <span class="keywordtype">bool</span> <a class="code" href="classpepr3d_1_1_geometry_utils.html#a6fe5d1ec681688da1e249a0f87a4944d">simplifyPolygon</a>(CGAL::Polygon_2&lt;K&gt;&amp; poly) {</div><div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;        <span class="keyword">using</span> Segment = CGAL::Segment_2&lt;K&gt;;</div><div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;</div><div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;        std::vector&lt;size_t&gt; verticesToRemove;</div><div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;        <span class="keyword">const</span> <span class="keywordtype">size_t</span> vertexCount = poly.vertices_end() - poly.vertices_begin();</div><div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;        <span class="keywordflow">for</span>(<span class="keywordtype">size_t</span> i = 0; i &lt; vertexCount; i++) {</div><div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;            <span class="keyword">auto</span> currentVertex = std::next(poly.vertices_circulator(), i);</div><div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;</div><div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;            <span class="keyword">const</span> <span class="keyword">typename</span> K::Line_2 neighbourLine(*std::prev(currentVertex), *std::next(currentVertex));</div><div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;            <span class="keywordflow">if</span>(neighbourLine.has_on(*currentVertex)) {</div><div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;                verticesToRemove.emplace_back(i);</div><div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;            }</div><div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;        }</div><div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;</div><div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;        <span class="comment">// Remove from the back so that we dont have to move that much data</span></div><div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;        <span class="keywordflow">for</span>(<span class="keyword">auto</span> it = verticesToRemove.rbegin(); it != verticesToRemove.rend(); ++it) {</div><div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;            <span class="keywordtype">size_t</span> vertexId = *it;</div><div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;            poly.erase(poly.vertices_begin() + vertexId);</div><div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;        }</div><div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;</div><div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;        <span class="keywordflow">return</span> !verticesToRemove.empty();</div><div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;    }</div><div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;</div><div class="line"><a name="l00073"></a><span class="lineno"><a class="line" href="classpepr3d_1_1_geometry_utils.html#aa40d71268a74cdeb820d931175f14df0">   73</a></span>&#160;    <span class="keyword">static</span> std::vector&lt;DataTriangle::K::Point_3&gt; <a class="code" href="classpepr3d_1_1_geometry_utils.html#aa40d71268a74cdeb820d931175f14df0">pointsOnCircle</a>(<span class="keyword">const</span> DataTriangle::K::Circle_3&amp; circle, <span class="keywordtype">int</span> segments) {</div><div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;        <span class="keyword">using</span> Point3 = DataTriangle::K::Point_3;</div><div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;        P_ASSERT(segments &gt;= 3);</div><div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;        P_ASSERT(!circle.is_degenerate());</div><div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;</div><div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;        <span class="keyword">auto</span> plane = circle.supporting_plane();</div><div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;        <span class="keyword">const</span> <span class="keywordtype">double</span> radius = sqrt(CGAL::to_double(circle.squared_radius()));</div><div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;        <span class="keyword">const</span> <span class="keyword">auto</span> xBase = plane.base1() / CGAL::sqrt(CGAL::to_double(plane.base1().squared_length()));</div><div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;        <span class="keyword">const</span> <span class="keyword">auto</span> yBase = plane.base2() / CGAL::sqrt(CGAL::to_double(plane.base2().squared_length()));</div><div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;</div><div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;        std::vector&lt;DataTriangle::K::Point_3&gt; points;</div><div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;</div><div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;        <span class="keywordflow">for</span>(<span class="keywordtype">size_t</span> i = 0; i &lt; segments; i++) {</div><div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;            <span class="keyword">const</span> <span class="keywordtype">double</span> circleCoord = (static_cast&lt;double&gt;(i) / segments) * 2 * glm::pi&lt;double&gt;();</div><div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;            <span class="keyword">const</span> Point3 pt = circle.center() + xBase * cos(circleCoord) * radius + yBase * sin(circleCoord) * radius;</div><div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;</div><div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;            points.push_back(pt);</div><div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;        }</div><div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;</div><div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;        <span class="keywordflow">return</span> points;</div><div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;    }</div><div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;</div><div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;    <span class="keyword">template</span> &lt;<span class="keyword">typename</span> K&gt;</div><div class="line"><a name="l00098"></a><span class="lineno"><a class="line" href="classpepr3d_1_1_geometry_utils.html#a376d662a35f0d4583276472d4576ae7b">   98</a></span>&#160;    <span class="keyword">static</span> CGAL::Orientation <a class="code" href="classpepr3d_1_1_geometry_utils.html#a376d662a35f0d4583276472d4576ae7b">shoelaceOrientationTest</a>(<span class="keyword">const</span> CGAL::Polygon_2&lt;K&gt;&amp; poly) {</div><div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;        <span class="keyword">typename</span> K::FT shoelaceSum = 0;</div><div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;</div><div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;        <span class="keyword">const</span> <span class="keywordtype">size_t</span> vertexCount = poly.vertices_end() - poly.vertices_begin();</div><div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;        <span class="keywordflow">for</span>(<span class="keywordtype">size_t</span> i = 0; i &lt; vertexCount; i++) {</div><div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;            <span class="keyword">auto</span> currentVertexIt = poly.vertices_circulator() + i;</div><div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;            <span class="keyword">auto</span> nextVertexIt = currentVertexIt + 1;</div><div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;</div><div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;            shoelaceSum += currentVertexIt-&gt;x() * nextVertexIt-&gt;y();</div><div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;            shoelaceSum -= currentVertexIt-&gt;y() * nextVertexIt-&gt;x();</div><div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;        }</div><div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;</div><div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;        <span class="keywordflow">if</span>(shoelaceSum &gt; 0)</div><div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;            <span class="keywordflow">return</span> CGAL::Orientation::COUNTERCLOCKWISE;</div><div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;        <span class="keywordflow">if</span>(shoelaceSum &lt; 0)</div><div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;            <span class="keywordflow">return</span> CGAL::Orientation::CLOCKWISE;</div><div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;</div><div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;        <span class="keywordflow">return</span> CGAL::Orientation::COLLINEAR;</div><div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;    }</div><div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;</div><div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;    <span class="keyword">template</span> &lt;<span class="keyword">typename</span> Traits_2&gt;</div><div class="line"><a name="l00120"></a><span class="lineno"><a class="line" href="classpepr3d_1_1_geometry_utils.html#ab7efa1cf650e08d63cfae3f9a7a5c067">  120</a></span>&#160;    <span class="keyword">static</span> <span class="keywordtype">bool</span> <a class="code" href="classpepr3d_1_1_geometry_utils.html#ab7efa1cf650e08d63cfae3f9a7a5c067">is_valid_polygon_with_holes</a>(<span class="keyword">const</span> <span class="keyword">typename</span> Traits_2::Polygon_with_holes_2&amp; pgn,</div><div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;                                            <span class="keyword">const</span> Traits_2&amp; traits) {</div><div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;        <span class="keywordtype">bool</span> closed = CGAL::is_closed_polygon_with_holes(pgn, traits);</div><div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;        CGAL_warning_msg(closed, <span class="stringliteral">&quot;The polygon&#39;s boundary or one of its holes is not closed.&quot;</span>);</div><div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;        <span class="keywordflow">if</span>(!closed)</div><div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;</div><div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;        <span class="keywordtype">bool</span> relatively_simple = CGAL::is_relatively_simple_polygon_with_holes(pgn, traits);</div><div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;        CGAL_warning_msg(relatively_simple, <span class="stringliteral">&quot;The polygon is not relatively simple.&quot;</span>);</div><div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;        <span class="keywordflow">if</span>(!relatively_simple)</div><div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;</div><div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;        <span class="keywordtype">bool</span> no_cross = CGAL::is_crossover_outer_boundary(pgn, traits);</div><div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;        CGAL_warning_msg(no_cross, <span class="stringliteral">&quot;The polygon has a crossover.&quot;</span>);</div><div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;        <span class="keywordflow">if</span>(!no_cross)</div><div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;</div><div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;        <span class="keywordtype">bool</span> valid_orientation = <a class="code" href="classpepr3d_1_1_geometry_utils.html#a0a4acf058ecff218c2f64cb92f6a4090">GeometryUtils::has_valid_orientation_polygon_with_holes</a>(pgn, traits);</div><div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;        CGAL_warning_msg(valid_orientation, <span class="stringliteral">&quot;The polygon has a wrong orientation.&quot;</span>);</div><div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;        <span class="keywordflow">if</span>(!valid_orientation)</div><div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;</div><div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;        <span class="keywordtype">bool</span> holes_disjoint = CGAL::are_holes_and_boundary_pairwise_disjoint(pgn, traits);</div><div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;        CGAL_warning_msg(holes_disjoint, <span class="stringliteral">&quot;Holes of the PWH intersect amongst themselves or with outer boundary&quot;</span>);</div><div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;        <span class="keywordflow">if</span>(!holes_disjoint)</div><div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;</div><div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;    }</div><div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;</div><div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;    <span class="keyword">template</span> &lt;<span class="keyword">typename</span> Traits_2&gt;</div><div class="line"><a name="l00151"></a><span class="lineno"><a class="line" href="classpepr3d_1_1_geometry_utils.html#a0a4acf058ecff218c2f64cb92f6a4090">  151</a></span>&#160;    <span class="keyword">static</span> <span class="keywordtype">bool</span> <a class="code" href="classpepr3d_1_1_geometry_utils.html#a0a4acf058ecff218c2f64cb92f6a4090">has_valid_orientation_polygon_with_holes</a>(<span class="keyword">const</span> <span class="keyword">typename</span> Traits_2::Polygon_with_holes_2&amp; pgn,</div><div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;                                                         <span class="keyword">const</span> Traits_2&amp; traits) {</div><div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;        <span class="keywordflow">if</span>(<a class="code" href="classpepr3d_1_1_geometry_utils.html#a376d662a35f0d4583276472d4576ae7b">shoelaceOrientationTest</a>(pgn.outer_boundary()) != CGAL::Orientation::COUNTERCLOCKWISE) {</div><div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;        }</div><div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;</div><div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;        <span class="keywordflow">for</span>(<span class="keyword">auto</span> holeIt = pgn.holes_begin(); holeIt != pgn.holes_end(); ++holeIt) {</div><div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;            <span class="keywordflow">if</span>(<a class="code" href="classpepr3d_1_1_geometry_utils.html#a376d662a35f0d4583276472d4576ae7b">shoelaceOrientationTest</a>(*holeIt) != CGAL::Orientation::CLOCKWISE) {</div><div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;                <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;            }</div><div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;        }</div><div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;</div><div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;    }</div><div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;</div><div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;    <span class="keyword">static</span> std::pair&lt;DataTriangle::K::Point_3, double&gt; <a class="code" href="classpepr3d_1_1_geometry_utils.html#a982761c1e66eb293064c3acbffe5ede3">getBoundingSphere</a>(</div><div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;        <span class="keyword">const</span> std::vector&lt;DataTriangle::K::Point_3&gt;&amp; shape);</div><div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;</div><div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;    <span class="keyword">static</span> std::pair&lt;DataTriangle::K::Point_3, double&gt; <a class="code" href="classpepr3d_1_1_geometry_utils.html#a982761c1e66eb293064c3acbffe5ede3">getBoundingSphere</a>(</div><div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;        <span class="keyword">const</span> std::vector&lt;DataTriangle::Triangle&gt;&amp; triangles);</div><div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;</div><div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;    <span class="keyword">static</span> std::pair&lt;DataTriangle::K::Point_3, double&gt; <a class="code" href="classpepr3d_1_1_geometry_utils.html#a982761c1e66eb293064c3acbffe5ede3">getBoundingSphere</a>(<span class="keyword">const</span> DataTriangle::Triangle&amp; triangle);</div><div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;</div><div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;    <span class="keyword">static</span> <span class="keywordtype">float</span> <a class="code" href="classpepr3d_1_1_geometry_utils.html#a3c0957732e9c372ca63b5271cf91d98d">segmentPointDistanceSquared</a>(<span class="keyword">const</span> glm::vec3&amp; start, <span class="keyword">const</span> glm::vec3&amp; end, <span class="keyword">const</span> glm::vec3&amp; point);</div><div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;</div><div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;    <span class="keyword">static</span> std::optional&lt;glm::vec3&gt; <a class="code" href="classpepr3d_1_1_geometry_utils.html#afee093fc93f94d5d7552611a34931ea2">triangleRayIntersection</a>(<span class="keyword">const</span> <span class="keyword">class</span> <a class="code" href="classpepr3d_1_1_data_triangle.html">DataTriangle</a>&amp; tri, ci::Ray ray);</div><div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;</div><div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;    <span class="keyword">static</span> <span class="keywordtype">bool</span> isFullyInsideASphere(<span class="keyword">const</span> DataTriangle::K::Triangle_3&amp; tri, <span class="keyword">const</span> DataTriangle::K::Point_3&amp; origin,</div><div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;                                     <span class="keywordtype">double</span> radius);</div><div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;</div><div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;    <span class="keyword">static</span> <span class="keywordtype">bool</span> isFullyInsideASphere(<span class="keyword">const</span> DataTriangle::K::Triangle_3&amp; tri, <span class="keyword">const</span> glm::vec3&amp; origin, <span class="keywordtype">double</span> radius) {</div><div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;        <span class="keywordflow">return</span> isFullyInsideASphere(tri, DataTriangle::K::Point_3(origin.x, origin.y, origin.z), radius);</div><div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;    }</div><div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;};</div><div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;</div><div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;}  <span class="comment">// namespace pepr3d</span></div><div class="ttc" id="classpepr3d_1_1_geometry_utils_html_a376d662a35f0d4583276472d4576ae7b"><div class="ttname"><a href="classpepr3d_1_1_geometry_utils.html#a376d662a35f0d4583276472d4576ae7b">pepr3d::GeometryUtils::shoelaceOrientationTest</a></div><div class="ttdeci">static CGAL::Orientation shoelaceOrientationTest(const CGAL::Polygon_2&lt; K &gt; &amp;poly)</div><div class="ttdoc">Determine orientation of a polygon using shoelace formula Replacement for potentionally buggy CGAL im...</div><div class="ttdef"><b>Definition:</b> GeometryUtils.h:98</div></div>
<div class="ttc" id="classpepr3d_1_1_geometry_utils_html_aa40d71268a74cdeb820d931175f14df0"><div class="ttname"><a href="classpepr3d_1_1_geometry_utils.html#aa40d71268a74cdeb820d931175f14df0">pepr3d::GeometryUtils::pointsOnCircle</a></div><div class="ttdeci">static std::vector&lt; DataTriangle::K::Point_3 &gt; pointsOnCircle(const DataTriangle::K::Circle_3 &amp;circle, int segments)</div><div class="ttdoc">Get equidistant points on circle.</div><div class="ttdef"><b>Definition:</b> GeometryUtils.h:73</div></div>
<div class="ttc" id="namespacepepr3d_html"><div class="ttname"><a href="namespacepepr3d.html">pepr3d</a></div><div class="ttdoc">Fix for CGAL bugs in polygon with holes verification Contained in CGAL PR #3688, likely to be in 4....</div><div class="ttdef"><b>Definition:</b> CmdColorManager.h:9</div></div>
<div class="ttc" id="classpepr3d_1_1_geometry_utils_1_1_tri_ray_int_visitor_html"><div class="ttname"><a href="classpepr3d_1_1_geometry_utils_1_1_tri_ray_int_visitor.html">pepr3d::GeometryUtils::TriRayIntVisitor</a></div><div class="ttdef"><b>Definition:</b> GeometryUtils.h:33</div></div>
<div class="ttc" id="classpepr3d_1_1_geometry_utils_html_a3c0957732e9c372ca63b5271cf91d98d"><div class="ttname"><a href="classpepr3d_1_1_geometry_utils.html#a3c0957732e9c372ca63b5271cf91d98d">pepr3d::GeometryUtils::segmentPointDistanceSquared</a></div><div class="ttdeci">static float segmentPointDistanceSquared(const glm::vec3 &amp;start, const glm::vec3 &amp;end, const glm::vec3 &amp;point)</div><div class="ttdoc">Find squared distance between a line segment and a point in 3D space.</div><div class="ttdef"><b>Definition:</b> GeometryUtils.cpp:11</div></div>
<div class="ttc" id="classpepr3d_1_1_geometry_utils_html_a6fe5d1ec681688da1e249a0f87a4944d"><div class="ttname"><a href="classpepr3d_1_1_geometry_utils.html#a6fe5d1ec681688da1e249a0f87a4944d">pepr3d::GeometryUtils::simplifyPolygon</a></div><div class="ttdeci">static bool simplifyPolygon(CGAL::Polygon_2&lt; K &gt; &amp;poly)</div><div class="ttdoc">Simplify polygon, removing unnecessary vertices.</div><div class="ttdef"><b>Definition:</b> GeometryUtils.h:49</div></div>
<div class="ttc" id="classpepr3d_1_1_data_triangle_html"><div class="ttname"><a href="classpepr3d_1_1_data_triangle.html">pepr3d::DataTriangle</a></div><div class="ttdoc">Custom Triangle type holding the CGAL::Triangle_3 and additional data.</div><div class="ttdef"><b>Definition:</b> Triangle.h:13</div></div>
<div class="ttc" id="classpepr3d_1_1_geometry_utils_html_a0a4acf058ecff218c2f64cb92f6a4090"><div class="ttname"><a href="classpepr3d_1_1_geometry_utils.html#a0a4acf058ecff218c2f64cb92f6a4090">pepr3d::GeometryUtils::has_valid_orientation_polygon_with_holes</a></div><div class="ttdeci">static bool has_valid_orientation_polygon_with_holes(const typename Traits_2::Polygon_with_holes_2 &amp;pgn, const Traits_2 &amp;traits)</div><div class="ttdef"><b>Definition:</b> GeometryUtils.h:151</div></div>
<div class="ttc" id="classpepr3d_1_1_geometry_utils_html_a982761c1e66eb293064c3acbffe5ede3"><div class="ttname"><a href="classpepr3d_1_1_geometry_utils.html#a982761c1e66eb293064c3acbffe5ede3">pepr3d::GeometryUtils::getBoundingSphere</a></div><div class="ttdeci">static std::pair&lt; DataTriangle::K::Point_3, double &gt; getBoundingSphere(const std::vector&lt; DataTriangle::K::Point_3 &gt; &amp;shape)</div><div class="ttdoc">Get min bounding sphere of a point shape.</div><div class="ttdef"><b>Definition:</b> GeometryUtils.cpp:49</div></div>
<div class="ttc" id="classpepr3d_1_1_geometry_utils_html"><div class="ttname"><a href="classpepr3d_1_1_geometry_utils.html">pepr3d::GeometryUtils</a></div><div class="ttdoc">Static utility functions that are not closely tied to Geometry.</div><div class="ttdef"><b>Definition:</b> GeometryUtils.h:28</div></div>
<div class="ttc" id="classpepr3d_1_1_geometry_utils_html_ab7efa1cf650e08d63cfae3f9a7a5c067"><div class="ttname"><a href="classpepr3d_1_1_geometry_utils.html#ab7efa1cf650e08d63cfae3f9a7a5c067">pepr3d::GeometryUtils::is_valid_polygon_with_holes</a></div><div class="ttdeci">static bool is_valid_polygon_with_holes(const typename Traits_2::Polygon_with_holes_2 &amp;pgn, const Traits_2 &amp;traits)</div><div class="ttdoc">Check validity of a polygon with holes using shoelace formula instead of a CGAL orientation test.</div><div class="ttdef"><b>Definition:</b> GeometryUtils.h:120</div></div>
<div class="ttc" id="classpepr3d_1_1_geometry_utils_html_afee093fc93f94d5d7552611a34931ea2"><div class="ttname"><a href="classpepr3d_1_1_geometry_utils.html#afee093fc93f94d5d7552611a34931ea2">pepr3d::GeometryUtils::triangleRayIntersection</a></div><div class="ttdeci">static std::optional&lt; glm::vec3 &gt; triangleRayIntersection(const class DataTriangle &amp;tri, ci::Ray ray)</div><div class="ttdoc">Find intersection point of a ray and a single triangle If the intersection is a segment return one of...</div><div class="ttdef"><b>Definition:</b> GeometryUtils.cpp:22</div></div>
</div><!-- fragment --></div><!-- contents -->
</div><!-- doc-content -->
<!-- start footer part -->
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
  <ul>
    <li class="navelem"><a class="el" href="dir_68267d1309a1af8e8297ef4c3efbcdba.html">src</a></li><li class="navelem"><a class="el" href="dir_405fd32de3649961a5f009c7a3fe84df.html">geometry</a></li><li class="navelem"><b>GeometryUtils.h</b></li>
    <li class="footer">Generated by
    <a href="http://www.doxygen.org/index.html">
    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.15 </li>
  </ul>
</div>
</body>
</html>
